FunctionApproximations`
FunctionApproximations`
MiniMaxApproximation
MiniMaxApproximation[expr,{x,{x0,x1},m,n}]
finds the rational polynomial function of x, with numerator order m and denominator order n, that gives a mini-max approximation to expr on the interval x0 to x1.
MiniMaxApproximation[expr,approx,{x,{x0,x1},m,n}]
finds the mini-max approximation to expr, starting the iterative algorithm with approx.
Details and Options
- To use MiniMaxApproximation, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].
- MiniMaxApproximation minimizes the maximum value of the relative error between the approximation and expr.
- MiniMaxApproximation returns {abscissa,{approximation,maxerror}}, where abscissa is a list of the abscissas where the relative error is a local maximum, approximation is the rational approximant, and maxerror is the global maximum of the relative error.
- When an approximation is given as the second argument of MiniMaxApproximation, it must have the same form as the result returned by MiniMaxApproximation.
- The following options can be given:
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Bias 0 bias in the automatic choice of interpolation points Brake {5,5} braking to apply on iterative algorithm Derivatives Automatic function to use for derivatives MaxIterations 20 maximum number of iterations to use PlotFlag False whether to plot relative error PrintFlag False whether to print status information WorkingPrecision MachinePrecision precision to use in internal computations